How to make an animated model jump in BGE
You can add Character type physics to your object.

Go to the Properties panel, and under the Physics tab, change the type from Static to Character and Check collision bounds; Depending on what your character looks like, you may want to change the Bounds type. As your character is rigged, you'll have to check Compound. You also can tweak the settings if you would like to modify the margin between objects, when colliding.